First Cohomology with Trivial Coefficients of All Unitary Easy Quantum Group Duals

TL;DR

This paper computes the first quantum group cohomology with trivial coefficients for the duals of all unitary easy quantum groups, including those with unknown partition categories, advancing understanding in quantum algebra.

Contribution

It provides a complete computation of the first cohomology for all such quantum groups, even those with previously unidentified partition categories.

Findings

First cohomology is explicitly computed for all duals of unitary easy quantum groups.

Includes cases with unknown associated partition categories.

Advances the understanding of quantum group cohomology structure.

Abstract

The first quantum group cohomology with trivial coefficients of the discrete dual of any unitary easy quantum group is computed. That includes those potential quantum groups whose associated categories of two-colored partitions have not yet been found.